Title

Eigenprojections and the equality of latent roots of a correlation matrix

Keywords

Chi-squared test; Principal components analysis

Abstract

In this paper, we consider the inference problem regarding the equality of the q smallest latent roots of a correlation matrix. A statistic, which is a function of the eigenprojection associated with the q smallest latent roots of the sample correlation matrix, is shown to have an asymptotic normal distribution. The expected value of this statistic is the zero vector if, and only if, the q smallest latent roots of the population correlation matrix are equal. This permits the construction of a chi-squared test statistic for the test of the equality of the q smallest latent roots of a population correlation matrix. Simulation results indicate that this test is superior to others currently in use in terms of achieving the nominal significance level for small sample sizes.

Publication Date

12-11-1996

Publication Title

Computational Statistics and Data Analysis

Volume

23

Issue

2

Number of Pages

229-238

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0167-9473(96)00033-3

Socpus ID

0042037856 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0042037856

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